It has been suggested that RNA viruses and other subcellular entities endowed with RNA genomes are relicts from an ancient RNA/protein World which is believed to have preceded extant DNA/RNA/protein-based cells. According to their proponents, this possibility is supported by the small-genome sizes of RNA viruses and their manifold replication strategies, which have been interpreted as the result of an evolutionary exploration of different alternative genome organizations and replication strategies during early evolutionary stages. At the other extreme are the giant DNA viruses, whose genome sizes can be as large as those of some prokaryotes, and which have been grouped by some authors into a fourth domain of life. As argued here, the comparative analysis of the chemical nature and sizes of the viral genomes reported in GenBank does not reveal any obvious correlation with the phylogenetic history of their hosts. Accordingly, it is somewhat difficult to reconcile the proposal of the putative pre-DNA antiquity of RNA viruses, with their extraordinary diversity in plant hosts and their apparent absence among the Archaea. Other issues related to the genome size of all known viruses and subviral agents and the relationship with their hosts are discussed.